Pith Number

pith:Z7UT4VFK

pith:2012:Z7UT4VFK2X3A44Y23BEYEOJFEE

not attested not anchored not stored refs pending

Tight complexes in 3-space admit perfect discrete Morse functions

Bruno Benedetti, Karim Adiprasito

arxiv:1202.3390 v2 · 2012-02-15 · math.GT · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z7UT4VFK2X3A44Y23BEYEOJFEE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:58:24.261806Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfe93e54aad5f60e731ad849823925213db28d1bf2556d6c1d137f8555ffcdbb

Aliases

arxiv: 1202.3390 · arxiv_version: 1202.3390v2 · doi: 10.48550/arxiv.1202.3390 · pith_short_12: Z7UT4VFK2X3A · pith_short_16: Z7UT4VFK2X3A44Y2 · pith_short_8: Z7UT4VFK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Z7UT4VFK2X3A44Y23BEYEOJFEE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: cfe93e54aad5f60e731ad849823925213db28d1bf2556d6c1d137f8555ffcdbb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd192d09784d0e114856189264af2526ea24f95bc474b8d8207ecc6abb9610ad",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-02-15T18:07:22Z",
    "title_canon_sha256": "2e25b136692e99d4567e842da1a52fd842df62a82b951a087276d1aa8051bd23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3390",
    "kind": "arxiv",
    "version": 2
  }
}